dorsal/arxiv
View SchemaQuantum Complexity of Testing Group Commutativity
| Authors | Frederic Magniez, Ashwin Nayak |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506265 |
| URL | https://arxiv.org/abs/quant-ph/0506265 |
Abstract
We consider the problem of testing the commutativity of a black-box group specified by its k generators. The complexity (in terms of k) of this problem was first considered by Pak, who gave a randomized algorithm involving O(k) group operations. We construct a quite optimal quantum algorithm for this problem whose complexity is in O (k^{2/3}). The algorithm uses and highlights the power of the quantization method of Szegedy. For the lower bound of Omega(k^{2/3}), we give a reduction from a special case of Element Distinctness to our problem. Along the way, we prove the optimality of the algorithm of Pak for the randomized model.
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"abstract": "We consider the problem of testing the commutativity of a black-box group\nspecified by its k generators. The complexity (in terms of k) of this problem\nwas first considered by Pak, who gave a randomized algorithm involving O(k)\ngroup operations. We construct a quite optimal quantum algorithm for this\nproblem whose complexity is in O (k^{2/3}). The algorithm uses and highlights\nthe power of the quantization method of Szegedy. For the lower bound of\nOmega(k^{2/3}), we give a reduction from a special case of Element Distinctness\nto our problem. Along the way, we prove the optimality of the algorithm of Pak\nfor the randomized model.",
"arxiv_id": "quant-ph/0506265",
"authors": [
"Frederic Magniez",
"Ashwin Nayak"
],
"categories": [
"quant-ph",
"cs.DS"
],
"title": "Quantum Complexity of Testing Group Commutativity",
"url": "https://arxiv.org/abs/quant-ph/0506265"
},
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